| You are thinking about one particle flowing through the radiator and changing the particle's temperature, instead of a constant flow of coolant existing inside the radiator and changing the radiator's temperature. Just imagine that the coolant is the same temperature throughout your entire system. Call this your average temperature, just like air in an oven. Now your coolant is flowing across the radiator, just like air in an oven. The coolant heats the radiator, just like air in an oven heats food. The hotter the radiator gets, the more heat that the air coming in can draw away from it. Now since the temperature of your coolant inside the radiator will always be the same (who cares what it is after if passes through the radiator, we're worried about heat being transfered to the radiator), the faster the coolant is moving inside the radiator, the faster the heat will be transfered. This is a standard fluids problem. An example that proves this theory is cross flow cooling. You have a cold water pipe and hot water pipe running parallel to each other and touching. If you run the two fluids in the same direction, it takes some distance X before the temperature in both tubes are the same. Since they are both flowing in the same direction relative to each other, their relative velocities are zero and the equilibrium distance is the same as if they aren't moving at all. If you run the fluids in opposite directions (but still parrallel to each other), the equilibrium distance will be cut to X/4 since they are moving with a relative velocity double of whatever flow rate they are at.
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